Finite Group Databasebeta

← C22⋊#564 #46137

Subgroups — C22⋊#564 #46137

Order 256.

933 conjugacy classes of subgroups.

The subgroup lattice has 229 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#564C211yesmaximal, characteristic, complemented
2C22×#125C211yesmaximal, characteristic
3#2851C212yesmaximal
4#2822C212yesmaximal, complemented
5#2726C214yesmaximal, complemented
6#2719C214yesmaximal, complemented
7#2719C214yesmaximal, complemented
8#2473C214yesmaximal
9#2473C214yesmaximal
10#2442C214yesmaximal
11#2382C211yesmaximal, characteristic, complemented
12#564—28no—
13C2×#125—28no—
14C2×#125C2211yescharacteristic
15C2×#125C2212yes—
16C2×#125C2212yes—
17C2×#125C2214yes—
18C2×#125C2214yes—
19C2×#125C2214yes—
20C2×#125C2214yes—
21C2×#125C2211yescharacteristic
22C22×C4⋊C4C2214yes—
23C22×C4⋊C4C2212yes—
24C22×C42C2211yescharacteristic
25#400C2214yes—
26#400C2214yes—
27#400C2214yes—
28#400C2214yes—
29#398C2214yes—
30#398C2214yes—
31#398C2214yes—
32#398C2214yes—
33#398C2214yes—
34#398C2214yes—
35#398C2214yes—
36#398C2214yes—
37#389C2212yes—
38#389C2212yes—
39#389C2214yes—
40#389C2214yes—
41#389C2214yes—
42#389C2214yes—
43#387C2214yes—
44#387C2214yes—
45#387C2214yes—
46#387C2214yes—
47#387C2214yes—
48#387C2214yes—
49#385C2214yes—
50#385C2214yes—
51#385C2214yes—
52#385C2214yes—
53#382C2212yes—
54#382C2214yes—
55#380C2212yes—
56#380C2212yes—
57#380C2214yes—
58C4×C22⋊C4C2214yes—
59C23×C4C2311yescharacteristic
60C23×C4C2314yes—
61C23×C4C2312yes—
62#125—28no—
63#125—216no—
64#125—216no—
65#125—216no—
66#125—216no—
67#125—24no—
68#125—28no—
69#125D418yes—
70C2×C4⋊C4—28no—
71C2×C4⋊C4—216no—
72C2×C4⋊C4C2314yes—
73C2×C4⋊C4C2314yes—
74C2×C4⋊C4C2314yes—
75C2×C4⋊C4C2314yes—
76C2×C4⋊C4C2312yes—
77C2×C4⋊C4C2314yes—
78C2×C4⋊C4C2312yes—
79C2×C4⋊C4C2312yes—
80C2×C4⋊C4C2314yes—
81C2×C4⋊C4C2314yes—
82C2×C4⋊C4C2314yes—
83C2×C4⋊C4C2314yes—
84C2×C4⋊C4C2314yes—
85C2×C4⋊C4C2312yes—
86C2×C4⋊C4C2312yes—
87C2×C4⋊C4C2314yes—
88C2×C4⋊C4C2314yes—
89C2×C4⋊C4C2314yes—
90C2×C4⋊C4C2314yes—
91C2×C4⋊C4C2312yes—
92C2×C4⋊C4C2314yes—
93C2×C22⋊C4C2314yes—
94C2×C22⋊C4C2314yes—
95C2×C42—24no—
96C2×C42C2314yes—
97C2×C42C2311yescharacteristic
98C2×C42C2312yes—
99C2×C42C2314yes—
100C2×C42C2311yescharacteristic
101#95C2314yes—
102#95C2314yes—
103#95C2314yes—
104#95C2314yes—
105#95C2314yes—
106#95C2314yes—
107#95C2314yes—
108#95C2314yes—
109#95C2314yes—
110#95C2314yes—
111#95C2314yes—
112#95C2314yes—
113#95C2314yes—
114#95C2314yes—
115C24C2411yescharacteristic
116C22×C4—22no—
117C22×C4—22no—
118C22×C4—22no—
119C22×C4—28no—
120C22×C4—24no—
121C22×C4—24no—
122C22×C4—28no—
123C22×C4—44no—
124C22×C4—42no—
125C22×C4C2414yes—
126C22×C4C2414yes—
127C22×C4C2412yes—
128C22×C4C2414yes—
129C22×C4C2414yes—
130C22×C4C2414yes—
131C22×C4C2411yescharacteristic
132C22×C4C2414yes—
133C22×C4C2412yes—
134C22×C4C2411yescharacteristic
135C4⋊C4—28no—
136C4⋊C4—28no—
137C4⋊C4—28no—
138C4⋊C4—28no—
139C4⋊C4—24no—
140C4⋊C4—24no—
141C4⋊C4—24no—
142C4⋊C4—28no—
143C4⋊C4—28no—
144C4⋊C4—28no—
145C4⋊C4—28no—
146C4⋊C4—28no—
147C4⋊C4—28no—
148C4⋊C4—44no—
149C4⋊C4—42no—
150C4⋊C4—42no—
151C4⋊C4—44no—
152C4⋊C4—44no—
153C4⋊C4—44no—
154C4⋊C4C2×D418yes—
155C4⋊C4C2×D4116yes—
156C22⋊C4—28no—
157C22⋊C4—28no—
158C42—24no—
159C42—22no—
160C42—28no—
161C42—44no—
162C42C2×D414yes—
163C23—21no—
164C23—21no—
165C23—22no—
166C232−1+412yes—
167C232−1+414yes—
168C23C2511yescharacteristic
169C2×C4—28no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—24no—
181C2×C4—24no—
182C2×C4—24no—
183C2×C4—24no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—24no—
187C2×C4—24no—
188C2×C4—22no—
189C2×C4—24no—
190C2×C4—24no—
191C2×C4—24no—
192C2×C4—24no—
193C2×C4—24no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—48no—
197C2×C4—416no—
198C2×C4C22×D412yes—
199C2×C4C22×D414yes—
200C2×C4C22×D418yes—
201C2×C42−1+412yes—
202C22—22no—
203C22—24no—
204C22—22no—
205C22—24no—
206C22#56414yescomplemented
207C22C23×D411yescharacteristic
208C22C2×2−1+411yescharacteristic
209C22C2×2−1+411yescharacteristic
210C22C2×2−1+412yes—
211C22#58512yes—
212C4—22no—
213C4—22no—
214C4—28no—
215C4—24no—
216C4—44no—
217C4—44no—
218C4—42no—
219C4—44no—
220C4—44no—
221C4—44no—
222C2—24no—
223C2#348611yescharacteristic
224C2#348912yes—
225C2C2×#56411yescharacteristic
226C2#355311yescharacteristic
227C2#356312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C25
prime radicalC24C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#564C2semidirect
4. #2822C2semidirect
5. #2726C2semidirect
6. #2719C2semidirect
7. #2719C2semidirect
11. #2382C2semidirect
206. C22#564semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#5642
C22×#1252
#28512
#28222
#27262
#27192
#24732
#24422
#23822